Obfuscation ⇒ (IND-CPA Security $ ot\Rightarrow$ Circular Security)
Antonio Marcedone, Claudio Orlandi · Lecture notes in computer science · 2014
Circular security is an important notion for public-key encryption schemes and is needed by several cryptographic protocols. In circular security the adversary is given an extra “hint” consisting of a cycle of encryption of secret keys i.e., \(\left(E_{pk_1}(sk_2),\ldots, E_{pk_n}(sk_1)\right)\) . A natural question is whether every IND-CPA encryption scheme is also circular secure. It is trivial to see that this is not the case when n = 1. In 2010 a separation for n = 2 was shown by [ABBC10,GH10] under standard assumptions in bilinear groups. In this paper we finally settle the question showing that for every n there exists an IND-CPA secure scheme which is not n -circular secure. Our result relies on the recent progress in cryptographic obfuscation. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.